An internal-combustion engine is known from the German patent 33 14 543 and has a cooling circuit which cools the cylinder head and the area of the cylinder at top dead center of the piston. Cooling and heating are in balance. The cooling circuit is here incorporated in the cylinder and cylinder head or is provided in the cast components. Consequently, manufacture of these components is labor-intensive and their cost is high. U.S. Pat. No. 4,729,347 discloses a combustion engine in which the lower regions of the cylinders are air-cooled and the cylinder heads are fluid-cooled by a complicated array of channels. Since the material of a cylinder head is welded to the cylinder, cooling of this area cannot be accomplished via the cooling channels normally built into the cylinder wall. Instead, an extra annular channel must be formed around the cylinder by means of a separate casing.